implementation of a fuzzy logic-based embedded system for ... · fuzzy logic systems g. oltean...

Fuzzy Logic Systems G. Oltean

Implementation of a Fuzzy Logic-Based Embedded System for Engine RPM

Control

(Speed Control)


Introduction

➢implements an embedded system for the

Engine RPM control based on a

development board

➢developed around an Arduino Mega board

➢fuzzy logic system as controller

➢offers an easy understanding of the main

concepts regarding embedded systems


System implementationBlock diagram


DC-Motor:➢ Gear ratio: 30:1

➢ Free run speed at 6V: 1000RPM

➢ Free run current at 6V: 120mA

➢ Stall current at 6V: 1600mA


Hall Effect Sensor

The Hall effect:

❖ the production of a voltage difference (the Hall voltage) across an electrical conductor:

✓ transverse to an electric current in the conductor

✓ an applied magnetic field perpendicular to the current.

[What is Hall Effect and How Hall Effect Sensors Work,

https://www.youtube.com/watch?v=wpAA3qeOYiI]

B


Hall Effect Sensor – cont.

[https://howtomechatronics.com/how

-it-works/electrical-engineering/hall-

effect-hall-effect-sensors-work/]


Quadrature Encoder:

• Six pole magnetic disk +PCB

• Dual Channel

• 12 counts/revolution

• 2.8V -18V

Output signal

of the encoder


Motor Driver:

• L298 - Dual Full Bridge Driver (H bridge)

• Middle class

• 2 Motors

• Sensors power supply


Motor Driver:

• L298 - Dual Full Bridge Driver (H bridge)

• Middle class

• 2 Motors

• Sensors power supply

How the RPM can be controlled?


ArduinoMega

Pinout LCD screen


The Arduino Mega board is the “brain” of the entire system.

It is primarily responsible for the update of the digital control signal u, at

every time instance.

The actual RPM, RPMk is read and the actual RPM error (errk) and change

of RPM error (cerrk) are updated, as follows:

ⅇ𝑟𝑟𝑘 = 𝑅𝑃𝑀𝑘 − 𝑅𝑃𝑀𝑟𝑒𝑓

𝑐ⅇ𝑟𝑟𝑘 = ⅇ𝑟𝑟𝑘 − ⅇ𝑟𝑟𝑘−1

where ⅇ𝑟𝑟𝑘−1 is the RPM error in the previous time instance.

The star of the entire system is the fuzzy logic controller, whose role is to

infer the best modification in the control signal, in every time instance.

The digital version of the actual control signal is updated using the relation:

𝑢𝑘 = 𝑢𝑘−1 + Δ𝑢𝑘


RPM computation➢To obtain the actual RPM:

❖a method based on a fixed time interval (time window) to

count the revolutions of the main motor shaft.

❖a counter is triggered at the initial time ti and it counts the

pulses received from the Hall effect sensor up to the final

increment tf.

❖The RPM is computed using the relation :

Cf - final value of the counter

Ci - initial value of the counter

Cr = 12 counts per revolution

Gr = 30, the gear ratio (30:1)

tf, ti – are measured in seconds

𝑅𝑃𝑀 = 1000 ∙ 60𝐶𝑓 − 𝐶𝑖𝑡𝑓 − 𝑡𝑖

1

𝐶𝑟

1

𝐺𝑟


RPM computation

Cf - final value of the counter

Ci - initial value of the counter

Cr = 12 counts per revolution

Gr = 30, the gear ratio (30:1)

tf, ti – are measured in milliseconds

𝑅𝑃𝑀 = 1000 ∙ 60𝐶𝑓 − 𝐶𝑖

𝑡𝑓 − 𝑡𝑖

1

𝐶𝑟

1

𝐺𝑟


The Fuzzy Logic Controller

➢ first-order Takagi-Sugeno

➢ two inputs errFls and cerrFls

➢ one output ΔuFls

Fuzzy sets for the inputs Fuzzy sets for the output


errFls

cerrFls Neg Zero Pos

Neg N N Z

Zero N Z P

Pos Z P P

Rule base of the

fuzzy logic system

Block diagram of the fuzzy logic controller


The defuzzification method, used to transform the partial output fuzzy sets resulted from the inference process into a crisp value is the weighted average method.


Control surface of the fuzzy logic controller

ou

tpu

t

cErr

Err


Control Circuit

Fuzzy

logic

system cerr + _

+ _

RPM ref

z

1

ΔuFls

- +

z

1

u

RPM

errFls

cerrFls

0

255 -1

+1

-1

+1 su

err se

sc

Δu Motor

Driver

DC

Motor ua


System setup


Experimental resultsRPM from 0 to 1000

rise time = 8.8 s;

max. positive error = 5 rpm ;

max. negative error = 5rpm;

RPM from 1000 to 500

fall time = 6.75 s;



RPM from 500 to 750

rise time = 4.75 s;



RPM from 750 to 0

fall time = 6.5 s;


To drastically decrease the time response of the control system,

the control strategy should be slightly modified.

Because the control characteristic of the DC motor driven by

the H-Bridge is almost liner, when a large variation of the motor

speed is required (larger than 60 rpm), the control signal is not

determined by the fuzzy logic system, but it is estimated by a

simple linear interpolation, that acts as a course adjustment of

the control signal.

Then, the fuzzy logic system regains its role for the fine

adjustment of the speed.

Decreasing the time response


Tracking mode operation: RPM tracks the temperature variation


Duty Cycle

23%

Low Speed

55%

Medium Speed

90%

High Speed

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